Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials

Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.) Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium

Received: 30 November 2006
Accepted: 27 April 2007

Abstract

We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and described by commutative or non-commutative tunneling operators. We show that the Hall-like transverse conductivity of such systems is quantized by relating the transverse conductivity to topological invariants known as Chern numbers. We show that this quantization is robust in non-Abelian potentials. The different integer values of this conductivity are explicitly computed for a specific non-Abelian system which leads to a fractal phase diagram.